In this application, we focus on the solution of three clinical problems involving image based planning and guidance of surgery or radiotherapy for the treatment of cancer. The application consists of three projects: 1. Image guided endovascular embolization of cranial tumors. 2. Biopsy via augmented reality. 3. Atlas-based segmentation for radiotherapy planning. Cores in Biostatistics, Facilities are also proposed. For these problems, medical images provide the information needed to guide the surgeon or radiotherapist in three dimensions as they plan or carry out the procedure. These images come from many modalities that are projective, 3D or tomographic and that are static or real-time. Planning or guiding the treatment involves the extraction, recognition, definition, and 3D display of anatomic or physiologic objects that are either the targets of the treatment or are to be avoided by the treatment beam, scalpel, needle, or other device. Frequently the presentations fuse information from multiple imaging modalities. Some methods require fused display in intraoperative time, fusing visual and medical imaging views of the patient. All of the methods require display control in interactive time, requiring the further development of interactive 3D display fusing extracted objects, models, and image intensities from one or more modalities and selecting structures for display based on anatomical relations. A class of figural object-based image analysis methods form a common support to the development of the approaches used for the image-based planning or guidance of surgery or radiotherapy. These image analysis methods have already allowed medical advances and are developed further in these projects. They combine previously available methods of deformable contours, figural graphs, and medial description and add a critical factor of stability and insensitivity to irrelevant detail based on medial measurement (cross-figural boundary linkage) with an aperture proportional to width. The proposed research will produce methods and systems that will allow significant advances a) in visualization of cerebral vasculature for neurosurgical planning an guidance, b) in the accuracy of ultrasound- guided breast and liver biopsy, in the range of physicians able to carry out this procedure, and in the range of targets amenable to image-guided needle biopsy and surgery, and c) in the availability of 3D radiation treatment planning due to greatly increased speed and repeatability of object definition. These methods and systems will be usable in a wide variety of other clinical problems involving planning or guidance of therapy, and the display and image analysis techniques will be extendible to many other problems requiring object definition and 3D/2D registration.